Contributions to Profile Monitoring and Multivariate Statistical Process Control

The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2004

Author dc:creator

• Williams, James Dickson

Chairs dc:contributor.committeechair

• Birch, Jeffrey B.
• Woodall, William H.

Committee members dc:contributor.committeemember

• Spitzner, Dan J.
• Anderson-Cook, Christine M.
• Vining, G. Geoffrey

• heteroscedasticity
• Hotelling's T² statistic
• lack-of-fit
• minimum volume ellipsoid
• nonlinear regression
• sample size
• successive differences
• vertical density profile
• bioassay
• false alarm rate
• functional data

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-12102004-150057

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30032